List Removals

Source: CSES

Version: Phuoc Hung OJ Extended

Problem Statement

You are given a list of $n$ integers. During the process, if the current list has $k$ elements, they are numbered from $1$ to $k$ in their current order.

There are exactly $n$ removals. At removal $i$, remove the element currently at position $p_i$ and print its value.

Input

The first line contains $n$.

The second line contains $x_1,x_2,\ldots,x_n$.

The third line contains $p_1,p_2,\ldots,p_n$, where $1\le p_i\le n-i+1$.

Output

Print the removed values in order.

Subtasks

• Subtask 1 — 20%: $1\le n\le 50$.
• Subtask 2 — 30%: $1\le n\le 5000$.
• Subtask 3 — 50%: $1\le n\le 2\cdot10^5$, $1\le x_i\le10^9$.

Examples

Input

5
2 6 1 4 2
3 1 3 1 1

Output

1 2 2 6 4

Explanation

The sample is processed in order; every printed item/line corresponds to an operation that requires output.